Mittal finished third on the podium after scoring 53 in the finals at the Belmont Shooting Centre.
Mohammed Asab, the other Indian shooter in the six-man finals, finished in the fourth position, a climbdown from the bronze medal he won in Glasgow four years ago.
The experienced James Willett was the first to be eliminated.
Mittal, the 26-year-old, who won silver medal in the World Championships in Moscow last year besides a silver and gold in the ISSF World Cups, rallied to finish fifth with 133 in the qualifying.
Mittal had to be contend with a fifth-place finish in the 2014 Games.
Asab shot 137 to get into a shoot-off with McMath in the qualification before finishing second.
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